True, he did keep his theory a "moving target." But that was not to accommodate emprirical test or data, but to avoid them.
As to his integrity, read "Marx: The Red Prussian" based in large part on his correspondence with F. Engels.
He apparently was neither a nice nor an ethical man.
In fact, according to the author, Leopold Schwartzschild (sp?), his nickname in his graduate student days was "the calf biter"!!!!
My reading of "On the Jewish Question" also sees it as antisemitic (self-hating?) and positing an identity between "Judaism" and "Capitalism."
Much as Weber later linked "Protestantism" (The Protestant Ethic)with (the Spirit of)"Capitalism."
... and positing an identity between "Judaism" and "Capitalism" ...Of all your claims this is the most laughable. The Jews of Marx's era were not capitalists; they were ghetto-dwellers, forced to live in the margins. Some became bankers-money-lenders-usurers, like the Rothschilds, but this was also an artifact of their exclusion from civil and economic life, as Jews were excluded from trades and schools.